<p>In recent years, the frequency of infectious diseases has surged globally, making contact tracing a crucial tool for controlling epidemics. It is essential to evaluate its role in controlling emerging infectious diseases from multiple dimensions. This study establishes a Continuous-Time Markov Chain (CTMC) model based on deterministic models, integrating branching process theory and the Gillespie algorithm to analyze and simulate disease extinction probabilities and transmission pathways. Theoretical analysis yields extinction thresholds: the control reproduction number for the deterministic model and the stochastic threshold for the CTMC model, along with their equivalence. Notably, when both thresholds exceed 1, the deterministic model predicts disease outbreaks, while the CTMC model shows an extinction probability dependent on the initial number of infected individuals and their categories (e.g., symptomatic or asymptomatic). The sensitivity analysis reveals that when the thresholds significantly exceed 1, enhanced contact tracing alone is insufficient to eradicate the epidemic. It must be complemented with additional interventions. Additionally, with the relaxation of social restrictions and the decline in hospitalization rate, strengthening contact tracing has become more necessary. While contact tracing has minimal impact on the deterministic threshold, it significantly affects the extinction probability in the CTMC model, particularly for symptomatic individuals. This emphasizes that strengthening contact tracing is crucial for disease extinction at low infection levels.</p>